Comparison between the rates of convergence of extremes under linear and under power normalization

Abstract

Regular variation, ℓ-max-stable laws, p-max-stable laws, Uniform metric, Total variation matric, Primary 60F05, 62E20, Secondary 62E15, 62G30,

Scaling of High-Quantile Estimators

“…We will adopt this idea of nonlinear norming and study the limit behavior of power normalized high-risk scenarios. Inspired by Barakat et al [2], who compared the convergence rates under Scaling of high-quantile estimators 971 linear and power normalizations within the block-maxima setting, we study the first-and secondorder asymptotic behaviors of power-normalized high-risk scenarios and quantiles. Definition 3.1.…”

On the rate of convergence to asymptotic independence between order statistics under power normalization with extension to the generalized order statistics

“…By using the theory of the second-order regular variation, Barakat et al. [4] studied the rates of convergence of the extremes under p-normalization to the each of the p−max stable laws. Moreover, a comparison between the rates of convergence under linear normalization (lnormalization) and p-normalization is done.…”

Bootstrap method for central and intermediate order statistics under power normalization

“…Therefore, using the power normalization, we get a wider class of limit df's which can be used in solving approximation problems. Another reason for using nonlinear normalization concerns the problem of refining the accuracy of approximation in the limit theorems using relatively non difficult monotone mappings in certain cases that can achieve a better rate of convergence (see Barakat et al [6]). Recently, Barakat et al [7], have tackled the problem of the mathematical modeling of extremes under power normalization.…”